Drift of scroll wave filaments in an anisotropic model of the left ventricle of the human heart

Scroll waves are three-dimensional vortices which occur in excitable media. Their formation in the heart results in the onset of cardiac arrhythmias, and the dynamics of their filaments determine the arrhythmia type. Most studies of filament dynamics were performed in domains with simple geometries and generic description of the anisotropy of cardiac tissue. Recently, we developed an analytical model of fibre structure and anatomy of the left ventricle (LV) of the human heart. Here, we perform a systematic study of the dynamics of scroll wave filaments for the cases of positive and negative tension in this anatomical model. We study the various possible shapes of LV and different degree of anisotropy of cardiac tissue. We show that, for positive filament tension, the final position of scroll wave filament is mainly determined by the thickness of the myocardial wall but, however, anisotropy attracts the filament to the LV apex. For negative filament tension, the filament buckles, and for most cases, tends to the apex of the heart with no or slight dependency on the thickness of the LV. We discuss the mechanisms of the observed phenomena and their implications for cardiac arrhythmias

Mathematical model of the anatomy and fibre orientation field of the left ventricle of the heart

Background: One of the main factors affecting propagation of electrical waves and contraction in ventricles of the heart is anisotropy of cardiac tissue. Anisotropy is determined by orientation of myocardial fibres. Determining fibre orientation field and shape of the heart is important for anatomically accurate modelling of electrical and mechanical function of the heart. The aim of this paper is to introduce a theoretical rule-based model for anatomy and fibre orientation of the left ventricle (LV) of the heart and to compare it with experimental data. We suggest explicit analytical formulae that allow us to obtain the left ventricle form and its fibre direction field. The ventricle band concept of cardiac architecture given by Torrent-Guasp is chosen as the model postulate. Methods: In our approach, anisotropy of the heart is derived from some general principles. The LV is considered as a set of identical spiral surfaces, each of which can be produced from the other by rotation around one vertical axis. Each spiral surface is filled with non-intersecting curves which represent myocardial fibres. For model verification, we use experimental data on fibre orientation in human and canine hearts. Results: LV shape and anisotropy are represented by explicit analytical expressions in a curvilinear 3-D coordinate system. The derived fibre orientation field shows good qualitative agreement with experimental data. The model reveals the most thorough quantitative simulation of fibre angles at the LV middle zone. Conclusions: Our analysis shows that the band concept can generate realistic anisotropy of the LV. Our model shows good qualitative agreement between the simulated fibre orientation field and the experimental data on LV anisotropy, and the model can be used for various numerical simulations to study the effects of anisotropy on cardiac excitation and mechanical function

Electrical wave propagation in an anisotropic model of the left ventricle based on analytical description of cardiac architecture.

We develop a numerical approach based on our recent analytical model of fiber structure in the left ventricle of the human heart. A special curvilinear coordinate system is proposed to analytically include realistic ventricular shape and myofiber directions. With this anatomical model, electrophysiological simulations can be performed on a rectangular coordinate grid. We apply our method to study the effect of fiber rotation and electrical anisotropy of cardiac tissue (i.e., the ratio of the conductivity coefficients along and across the myocardial fibers) on wave propagation using the ten Tusscher-Panfilov (2006) ionic model for human ventricular cells. We show that fiber rotation increases the speed of cardiac activation and attenuates the effects of anisotropy. Our results show that the fiber rotation in the heart is an important factor underlying cardiac excitation. We also study scroll wave dynamics in our model and show the drift of a scroll wave filament whose velocity depends non-monotonically on the fiber rotation angle; the period of scroll wave rotation decreases with an increase of the fiber rotation angle; an increase in anisotropy may cause the breakup of a scroll wave, similar to the mother rotor mechanism of ventricular fibrillation

Slow force response and auto-regulation of contractility in heterogeneous myocardium

Classically, the slow force response (SFR) of myocardium refers to slowly developing changes in cardiac muscle contractility induced by external mechanical stimuli, e.g. sustained stretch. We present evidence for an intra-myocardial SFR (SFRIM), caused by the internal mechanical interactions of muscle segments in heterogeneous myocardium. Here we study isometric contractions of a pair of end-to-end connected functionally heterogeneous cardiac muscles (an in-series muscle duplex). Duplex elements can be either biological muscles (BM), virtual muscles (VM), or a hybrid combination of BM and VM. The VM implements an Ekaterinburg-Oxford mathematical model accounting for the ionic and myofilament mechanisms of excitation-contraction coupling in cardiomyocytes. SFRIM is expressed in gradual changes in the overall duplex force and in the individual contractility of each muscle, induced by cyclic auxotonic deformations of coupled muscles. The muscle that undergoes predominant cyclic shortening shows force enhancement upon return to its isometric state in isolation, whereas average cyclic lengthening may decrease the individual muscle contractility. The mechanical responses are accompanied with slow and opposite changes in the shape and duration of both the action potential and Ca2+ transient in the cardiomyocytes of interacting muscles. Using the mathematical model we found that the contractility changes in interacting muscles follow the alterations in the sarcoplasmic reticulum loading in cardiomyocytes which result from the length-dependent Ca2+ activation of myofilaments and intracellular mechano-electrical feedback. The SFRIM phenomena unravel an important mechanism of cardiac functional auto-regulation applicable to the heart in norm and pathology, especially to hearts with severe electrical and/or mechanical dyssynchrony. © 2012 Elsevier Ltd